# Trying to grasp the idea

• kmkindig
In summary, the problem is asking for the velocity of liquid in a 2.0 cm diameter restriction in a pipe with a 4.0 cm diameter. The concept of continuity is used to solve this problem, where the mass flow rate into a control volume must equal the mass flow rate out in order to maintain a constant mass. By applying the principle Av=constant, it is determined that the velocity in the restriction is not 4.0 m/s, unless there is a mistake in the given information.

## Homework Statement

Liquid flows through a 4.0 cm diameter pipe at 1.0 m/s. there is a 2.0 cm diameter restriction in the line. What is the liquids velocity in this restriction?

## The Attempt at a Solution

I know that solution is 4.0 m/s but in don't know how to get there. Thank you

The concept one is concerned with here is continuity. For an incompressible fluid, the mass flow (rate) into a control volume must equal the mass flow (rate) out, otherwise mass would accumulate or decrease in the volume.

The mass flow rate is given by ρVA, where ρ is the fluid density, V is the mean (average) velocity and A is the cross-sectional area.

So we have ρVA(in) = ρVA(out), or ρVA(in) - ρVA(out) = 0, i.e. no net gain or loss of fluid (mass).

Now if ρ(in) = ρ(out), then the continuity equation becomes, V(in)A(in) = V(out)A(out).

Try apply this to given problem.

kmkindig said:
Liquid flows through a 4.0 cm diameter pipe at 1.0 m/s. there is a 2.0 cm diameter restriction in the line. What is the liquids velocity in this restriction?

I know the answer is 4.0 m/s but I am not for sure how to get there. A little help would be greatly appreciated. Thank you!

There is a principle that states Av=constant, where A is the area of the fluid's path at a given time and v is the velocity.
Hence the answer is not 4.0 m/s, unless I'm wrong.

## What does it mean to "grasp the idea"?

Grasping the idea refers to fully understanding or comprehending a concept or theory. It involves being able to explain and apply the idea in various contexts.

## Why is it important to grasp the idea?

Grasping the idea is important because it allows for deeper learning and critical thinking. It also helps in retaining information and being able to apply it in real-world situations.

## What are some strategies for trying to grasp an idea?

Some strategies for trying to grasp an idea include breaking it down into smaller parts, making connections to prior knowledge, and actively engaging with the material through practice and reflection.

## How can one improve their ability to grasp ideas?

Improving one's ability to grasp ideas can be done through regular practice and repetition, seeking clarification when needed, and actively seeking out different perspectives and approaches to understanding the idea.

## What should one do if they are having difficulty grasping an idea?

If someone is having difficulty grasping an idea, they can try different approaches such as seeking out additional resources or discussing the idea with others. It may also be helpful to take a break and come back to the idea with a fresh perspective.